integral of ((x^2)/4+2x+3)

Lösung

\int (\frac{x ^{2}}{4} + 2 x + 3) d x

\frac{x ^{3}}{12} + x^{2} + 3 x + C

Schritte zur Lösung

\int \frac{x ^{2}}{4} + 2 x + 3 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x ^{2}}{4} d x + \int 2 x d x + \int 3 d x

\int \frac{x ^{2}}{4} d x = \frac{x ^{3}}{12}

\int 2 x d x = x^{2}

\int 3 d x = 3 x

= \frac{x ^{3}}{12} + x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{12} + x^{2} + 3 x + C

\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

\frac{d}{d x} ((ln (x))^{2} (sin (x)))

(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0

d er i v a t i v e sin (x) cos (x) - sin^{2} (x) + x